Bunuel wrote:
If \(x < 0\), is \(\frac{y}{x} < 1\) ?
(1) \(y < x\)
(2) \(y < 0\)
Target question: Is \(\frac{y}{x} < 1\) ?This is a good candidate for
rephrasing the target question.
Since x is NEGATIVE, we can take:
\(\frac{y}{x} < 1\)...
...and multiply both sides by x to get:
\(y > x\) [aside: since we multiplied both sides of an inequality by a negative value, we reverse the direction of the inequality symbol]REPHRASED target question: Is \(y > x\) ?Aside: Here’s a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat-data-sufficiency?id=1100Once we've rephrased the target question, we can easily deal with the two statements
Statement 1: \(y < x\) So, the answer to the REPHRASED target question is
NO, y is NOT greater than xSince we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: \(y < 0\)So we now know that x and y are both negative.
This is not enough information to answer the REPHRASED target question. Here are two possible cases:
Case a: x = -1 and y = -2. In this case, the answer to the REPHRASED target question is
NO, y is NOT greater than xCase b: x = -2 and y = -1. In this case, the answer to the REPHRASED target question is
YES, y IS greater than xSince we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent